Did Hermione have what we would consider Eidetic memory? I think she didn't, because I think there's somewhere in the books where she says that she forgot something.
No. Her memory is very good, she has near-total recall, but it isn't perfect.
For instance, in Harry Potter and the Sorcerer's Stone Hermione says, "I'm trying to remember how to kill it" about the Devil's Snare.
If she had an eidectic memory, she'd have remembered what Professor Sprout said word-for-word and wouldn't have gotten only half of it ('likes dark and damp').
Hermione explicitly states that she cannot remember something:
Chamber of Secrets Chapter 9
Hermione emerged from between the bookshelves.
She looked irritable and at last seemed ready to talk to them.
“All the copies of Hogwarts, A History have been taken out,” she said, sitting down next to Harry and Ron. “And there’s a two-week waiting list. I wish I hadn’t left my copy at home, but I couldn’t fit it in my trunk with all the Lockhart books.”
“Why do you want it?” said Harry.
“The same reason everyone else wants it,” said Hermione, “to read up on the legend of the Chamber of Secrets.”
“What’s that?” said Harry quickly.
“That’s just it. I can’t remember,” said Hermione, biting her lip. “And I can’t find the story anywhere else — ”